During the course of drilling offshore wells from floating rigs or other water surface installations a common practice is to suspend the well casing strings from hangers supported in a wellhead housing at the floor of the sea or other body of water, and to pressure seal the annuli between the housing and the hangers by seal assemblies called packoffs. From earlier techniques involving running and installing a hanger and its packoff in separate round trips to the wellhead, the industry has developed tools and techniques for accomplishing the installation of both the hanger and its packoff in a single trip, thereby achieving significant savings in time and other expense. However, premature engagement of the packoff with the hanger, and obstruction of the packoff setting/sealing mechanisms by debris, have presented problems in use of these single trip tools and thus less than satisfactory results with their performance. The present invention was conceived and developed to overcome these problems, which it does in a novel and highly successful manner.